Dyson swarm algorithm inspired by the Dyson sphere megastructure model. This swarm model will be created via satellite-like and particle swarm optimization behaviors.
The base model is inspired by Particle Swarm Optimization as an algorithmic foundation. The following is the result of that animated base model.
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
def f(x, y):
"Objective Function"
return (x-3.14)**2 + (y-2.72)**2 + np.sin(3*x+1.41) + np.sin(4*y-1.73)
# Cpmpute and plot the function in 3 dimensions within [0,5][0,5]
x, y = np.array(np.meshgrid(np.linspace(0,5,100), np.linspace(0,5,100)))
z = f(x, y)
# Find the global minimum
x_min = x.ravel()[z.argmin()]
y_min = y.ravel()[z.argmin()]
# Hyper-parameter of the algorithm
c1 = c2 = 0.1
w = 0.8
# Create particles
n_particles = 20
np.random.seed(100)
X = np.random.rand(2, n_particles) * 5
V = np.random.randn(2, n_particles) * 0.1
# Initialize data
pbest = X
pbest_obj = f(X[0], X[1])
gbest = pbest[:, pbest_obj.argmin()]
gbest_obj = pbest_obj.min()
def update():
"Function to do one iteration of particle swarm optimization"
global V, X, pbest, pbest_obj, gbest, gbest_obj
# Update parameters
r1, r2 = np.random.rand(2)
V = w * V + c1*r1*(pbest - X) + c2*r2*(gbest.reshape(-1,1)-X)
X = X + V
obj = f(X[0], X[1])
pbest[:, (pbest_obj >= obj)] = X[:, (pbest_obj >= obj)]
pbest_obj = np.array([pbest_obj, obj]).min(axis=0)
gbest = pbest[:, pbest_obj.argmin()]
gbest_obj = pbest_obj.min()
# Set up base figure: The contour map
fig, ax = plt.subplots(figsize=(8,6))
fig.set_tight_layout(True)
img = ax.imshow(z, extent=[0, 5, 0, 5], origin='lower', cmap='viridis', alpha=0.5)
fig.colorbar(img, ax=ax)
ax.plot([x_min], [y_min], marker='x', markersize=5, color="white")
contours = ax.contour(x, y, z, 10, colors='black', alpha=0.4)
ax.clabel(contours, inline=True, fontsize=8, fmt="%.0f")
pbest_plot = ax.scatter(pbest[0], pbest[1], marker='o', color='black', alpha=0.5)
p_plot = ax.scatter(X[0], X[1], marker='o', color='blue', alpha=0.5)
p_arrow = ax.quiver(X[0], X[1], V[0], V[1], color='blue', width=0.005, angles='xy', scale_units='xy', scale=1)
gbest_plot = plt.scatter([gbest[0]], [gbest[1]], marker='*', s=100, color='black', alpha=0.4)
ax.set_xlim([0,5])
ax.set_ylim([0,5])
def animate(i):
"Steps of PSO: algorithm update and show in plot"
title = 'Iteration {:02d}'.format(i)
# Update parameters
update()
# Set picture
ax.set_title(title)
pbest_plot.set_offsets(pbest.T)
p_plot.set_offsets(X.T)
p_arrow.set_offsets(X.T)
p_arrow.set_UVC(V[0], V[1])
gbest_plot.set_offsets(gbest.reshape(1,-1))
return ax, pbest_plot, p_plot, p_arrow, gbest_plot
anim = FuncAnimation(fig, animate, frames=list(range(1,50)), interval=500, blit=False, repeat=True)
anim.save("PSO.gif", dpi=120, writer="pillow")
print("PSO found best solution at f({})={}".format(gbest, gbest_obj))
print("Global optimal at f({})={}".format([x_min,y_min], f(x_min,y_min)))